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Algebraic preconditioning for Biot-Barenblatt poroelastic systems

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Abstract

Poroelastic systems describe fluid flow through porous medium coupled with deformation of the porous matrix. In this paper, the deformation is described by linear elasticity, the fluid flow is modelled as Darcy flow. The main focus is on the Biot-Barenblatt model with double porosity/double permeability flow, which distinguishes flow in two regions considered as continua. The main goal is in proposing block diagonal preconditionings to systems arising from the discretization of the Biot-Barenblatt model by a mixed finite element method in space and implicit Euler method in time and estimating the condition number for such preconditioning. The investigation of preconditioning includes its dependence on material coefficients and parameters of discretization.

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Authors and Affiliations

  1. Institute of Geonics, Czech Academy of Sciences, Studenstká 1768, 708 00, Ostrava, Czech Republic

    Radim Blaheta & Tomáš Luber

Authors
  1. Radim Blaheta
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  2. Tomáš Luber
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Corresponding author

Correspondence to Radim Blaheta.

Additional information

The work was done within the projects LD15105 “Ultrascale computing in geo-sciences” and LQ1602 “IT4Innovations excellence in science” supported by the Ministry of Education, Youth and Sports of the Czech Republic.

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Blaheta, R., Luber, T. Algebraic preconditioning for Biot-Barenblatt poroelastic systems. Appl Math 62, 561–577 (2017). https://doi.org/10.21136/AM.2017.0179-17

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  • DOI: https://doi.org/10.21136/AM.2017.0179-17

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